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Problem 60 Easy Difficulty

Use Property 8 to estimate the value of the integral.

$ \displaystyle \int^3_0 \frac{1}{x + 4} \,dx $


$\frac{3}{7} \leq \int_{0}^{3} \frac{1}{x+4} d x \leq \frac{3}{4}$

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Video Transcript

because of the fact that one over X plus four is decreasing on the interval. We know that 1/7 is less than one over X plus four, which is less than or equal to one for. Therefore, we know 17 times three months here, which is 3/7 is less than equal to the integral from 0 to 3 one over X plus four DX, which is less than or equal to 14 times three minutes here, which just 1/4 times three, which is simply 3/4.